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Homework Help: How do I know if this field has a mass term?

  1. Sep 17, 2007 #1
    1. Special Relativity

    2. The problem statement, all variables and given/known data
    Consider this Lagrangian:

    L=(1/2) (\partial_{\mu} \Psi)(\partial^{mu} \Psi) + \exp(-(a\times \Psi)^2)

    Have this field a mass term?

    2. Relevant equations

    3. The attempt at a solution
  2. jcsd
  3. Sep 17, 2007 #2


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    Is this what one intended to write, or is this given in some text?

    [tex]L= \frac{1}{2} (\partial_{\mu} \Psi)(\partial^{\mu} \Psi) + e^{-{(a \Psi)}^2} [/tex]
  4. Sep 17, 2007 #3
    Yes, exactly this Lagrangian, where \Psi is a scalar field.
    Last edited: Sep 17, 2007
  5. Sep 17, 2007 #4


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    This is a nonlinear field theory so, strictly speaking, there is no clear meaning for a mass term.
    But I am guessing that they want you to treat the parameter "a" as small and to do a Taylor expansion of the exponential. If you do that, you will generate a mass term.

    That's my guess.
  6. Sep 17, 2007 #5


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    Well, just one question, you have the lagrangian, what are the field eqn's ?
  7. Sep 17, 2007 #6
    Do you mean the motion equations?
  8. Sep 17, 2007 #7
    Thanks, I'll think about this...
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